LMFDB - Embedded newform 435.2.c.e.349.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(349,435)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("435.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.3899266318336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} + 6x^{7} + 19x^{6} - 12x^{5} + 4x^{4} + 2x^{3} + 9x^{2} - 6x + 2 $ x^10 - 2x^9 + 2x^8 + 6x^7 + 19x^6 - 12x^5 + 4x^4 + 2x^3 + 9x^2 - 6*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.5
Root			$0.561843 + 0.561843i$ of defining polynomial
Character	$\chi$	$=$	435.349
Dual form			435.2.c.e.349.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.712495i q^{2} -1.00000i q^{3} +1.49235 q^{4} +(2.01848 - 0.962154i) q^{5} -0.712495 q^{6} +2.77986i q^{7} -2.48828i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.712495i q^{2} -1.00000i q^{3} +1.49235 q^{4} +(2.01848 - 0.962154i) q^{5} -0.712495 q^{6} +2.77986i q^{7} -2.48828i q^{8} -1.00000 q^{9} +(-0.685530 - 1.43816i) q^{10} +4.26814 q^{11} -1.49235i q^{12} +0.779856i q^{13} +1.98063 q^{14} +(-0.962154 - 2.01848i) q^{15} +1.21181 q^{16} +1.90354i q^{17} +0.712495i q^{18} -6.72036 q^{19} +(3.01228 - 1.43587i) q^{20} +2.77986 q^{21} -3.04103i q^{22} +2.17168i q^{23} -2.48828 q^{24} +(3.14852 - 3.88418i) q^{25} +0.555643 q^{26} +1.00000i q^{27} +4.14852i q^{28} -1.00000 q^{29} +(-1.43816 + 0.685530i) q^{30} -8.82061 q^{31} -5.83998i q^{32} -4.26814i q^{33} +1.35626 q^{34} +(2.67465 + 5.61108i) q^{35} -1.49235 q^{36} -1.48402i q^{37} +4.78822i q^{38} +0.779856 q^{39} +(-2.39411 - 5.02255i) q^{40} -7.71389 q^{41} -1.98063i q^{42} -8.19624i q^{43} +6.36956 q^{44} +(-2.01848 + 0.962154i) q^{45} +1.54731 q^{46} +5.19381i q^{47} -1.21181i q^{48} -0.727598 q^{49} +(-2.76746 - 2.24330i) q^{50} +1.90354 q^{51} +1.16382i q^{52} -11.7853i q^{53} +0.712495 q^{54} +(8.61515 - 4.10661i) q^{55} +6.91707 q^{56} +6.72036i q^{57} +0.712495i q^{58} +4.46028 q^{59} +(-1.43587 - 3.01228i) q^{60} -5.24905 q^{61} +6.28464i q^{62} -2.77986i q^{63} -1.73733 q^{64} +(0.750341 + 1.57412i) q^{65} -3.04103 q^{66} +8.49375i q^{67} +2.84075i q^{68} +2.17168 q^{69} +(3.99787 - 1.90567i) q^{70} +0.663102 q^{71} +2.48828i q^{72} +16.5345i q^{73} -1.05736 q^{74} +(-3.88418 - 3.14852i) q^{75} -10.0291 q^{76} +11.8648i q^{77} -0.555643i q^{78} -9.54554 q^{79} +(2.44602 - 1.16595i) q^{80} +1.00000 q^{81} +5.49611i q^{82} -0.0123998i q^{83} +4.14852 q^{84} +(1.83150 + 3.84226i) q^{85} -5.83978 q^{86} +1.00000i q^{87} -10.6203i q^{88} +5.46783 q^{89} +(0.685530 + 1.43816i) q^{90} -2.16789 q^{91} +3.24091i q^{92} +8.82061i q^{93} +3.70056 q^{94} +(-13.5649 + 6.46602i) q^{95} -5.83998 q^{96} +0.952006i q^{97} +0.518410i q^{98} -4.26814 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{4} + 6 q^{6} - 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^4 + 6 * q^6 - 10 * q^9	$ 10 q - 10 q^{4} + 6 q^{6} - 10 q^{9} + 4 q^{10} + 24 q^{11} - 12 q^{14} + 2 q^{15} + 2 q^{16} + 4 q^{19} + 8 q^{20} + 16 q^{21} - 18 q^{24} + 2 q^{25} - 10 q^{29} - 18 q^{30} + 4 q^{31} - 8 q^{34} + 2 q^{35} + 10 q^{36} - 4 q^{39} - 14 q^{40} - 28 q^{41} - 40 q^{44} - 12 q^{46} + 14 q^{49} - 12 q^{50} - 6 q^{54} + 2 q^{55} - 4 q^{56} - 8 q^{59} - 2 q^{60} - 24 q^{61} + 18 q^{64} + 6 q^{65} + 28 q^{66} - 16 q^{69} + 20 q^{70} + 60 q^{71} - 4 q^{74} + 12 q^{75} - 88 q^{76} + 36 q^{79} - 30 q^{80} + 10 q^{81} + 12 q^{84} - 14 q^{85} + 60 q^{86} + 44 q^{89} - 4 q^{90} - 24 q^{91} + 100 q^{94} - 36 q^{95} + 2 q^{96} - 24 q^{99}+O(q^{100}) $ 10 * q - 10 * q^4 + 6 * q^6 - 10 * q^9 + 4 * q^10 + 24 * q^11 - 12 * q^14 + 2 * q^15 + 2 * q^16 + 4 * q^19 + 8 * q^20 + 16 * q^21 - 18 * q^24 + 2 * q^25 - 10 * q^29 - 18 * q^30 + 4 * q^31 - 8 * q^34 + 2 * q^35 + 10 * q^36 - 4 * q^39 - 14 * q^40 - 28 * q^41 - 40 * q^44 - 12 * q^46 + 14 * q^49 - 12 * q^50 - 6 * q^54 + 2 * q^55 - 4 * q^56 - 8 * q^59 - 2 * q^60 - 24 * q^61 + 18 * q^64 + 6 * q^65 + 28 * q^66 - 16 * q^69 + 20 * q^70 + 60 * q^71 - 4 * q^74 + 12 * q^75 - 88 * q^76 + 36 * q^79 - 30 * q^80 + 10 * q^81 + 12 * q^84 - 14 * q^85 + 60 * q^86 + 44 * q^89 - 4 * q^90 - 24 * q^91 + 100 * q^94 - 36 * q^95 + 2 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	0.712495i		−	0.503810i	−0.967752	−	0.251905i	$-0.918943\pi$
$2$		−	0.712495i		−	0.503810i	0.967752	−	0.251905i	$-0.0810571\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.49235			0.746175
$5$	2.01848	−	0.962154i	0.902692	−	0.430288i
$5$	2.01848	−	0.962154i	0.902692	−	0.430288i
$6$	−0.712495			−0.290875
$7$			2.77986i			1.05069i	0.850890	+	0.525343i	$0.176063\pi$
$7$			2.77986i			1.05069i	−0.850890	+	0.525343i	$0.823937\pi$
$8$		−	2.48828i		−	0.879741i
$9$	−1.00000			−0.333333
$10$	−0.685530	−	1.43816i	−0.216784	−	0.454785i
$11$	4.26814			1.28689			0.643446	−	0.765491i	$-0.277504\pi$
$11$	4.26814			1.28689			0.643446	+	0.765491i	$0.277504\pi$
$12$		−	1.49235i		−	0.430805i
$13$			0.779856i			0.216293i	0.994135	+	0.108147i	$0.0344916\pi$
$13$			0.779856i			0.216293i	−0.994135	+	0.108147i	$0.965508\pi$
$14$	1.98063			0.529347
$15$	−0.962154	−	2.01848i	−0.248427	−	0.521169i
$16$	1.21181			0.302953
$17$			1.90354i			0.461677i	0.972992	+	0.230838i	$0.0741469\pi$
$17$			1.90354i			0.461677i	−0.972992	+	0.230838i	$0.925853\pi$
$18$			0.712495i			0.167937i
$19$	−6.72036			−1.54176			−0.770878	−	0.636983i	$-0.780182\pi$
$19$	−6.72036			−1.54176			−0.770878	+	0.636983i	$0.780182\pi$
$20$	3.01228	−	1.43587i	0.673566	−	0.321071i
$21$	2.77986			0.606614
$22$		−	3.04103i		−	0.648349i
$23$			2.17168i			0.452827i	0.974031	+	0.226413i	$0.0727000\pi$
$23$			2.17168i			0.452827i	−0.974031	+	0.226413i	$0.927300\pi$
$24$	−2.48828			−0.507919
$25$	3.14852	−	3.88418i	0.629704	−	0.776835i
$26$	0.555643			0.108971
$27$			1.00000i			0.192450i
$28$			4.14852i			0.783997i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$	−1.43816	+	0.685530i	−0.262570	+	0.125160i
$31$	−8.82061			−1.58423			−0.792114	−	0.610373i	$-0.791020\pi$
$31$	−8.82061			−1.58423			−0.792114	+	0.610373i	$0.791020\pi$
$32$		−	5.83998i		−	1.03237i
$33$		−	4.26814i		−	0.742988i
$34$	1.35626			0.232597
$35$	2.67465	+	5.61108i	0.452098	+	0.948446i
$36$	−1.49235			−0.248725
$37$		−	1.48402i		−	0.243971i	−0.992532	−	0.121986i	$-0.961074\pi$
$37$		−	1.48402i		−	0.243971i	0.992532	−	0.121986i	$-0.0389262\pi$
$38$			4.78822i			0.776752i
$39$	0.779856			0.124877
$40$	−2.39411	−	5.02255i	−0.378542	−	0.794135i
$41$	−7.71389			−1.20471			−0.602354	−	0.798229i	$-0.705770\pi$
$41$	−7.71389			−1.20471			−0.602354	+	0.798229i	$0.705770\pi$
$42$		−	1.98063i		−	0.305618i
$43$		−	8.19624i		−	1.24991i	−0.780659	−	0.624957i	$-0.785116\pi$
$43$		−	8.19624i		−	1.24991i	0.780659	−	0.624957i	$-0.214884\pi$
$44$	6.36956			0.960247
$45$	−2.01848	+	0.962154i	−0.300897	+	0.143429i
$46$	1.54731			0.228139
$47$			5.19381i			0.757595i	0.925480	+	0.378798i	$0.123662\pi$
$47$			5.19381i			0.757595i	−0.925480	+	0.378798i	$0.876338\pi$
$48$		−	1.21181i		−	0.174910i
$49$	−0.727598			−0.103943
$50$	−2.76746	−	2.24330i	−0.391377	−	0.317251i
$51$	1.90354			0.266549
$52$			1.16382i			0.161393i
$53$		−	11.7853i		−	1.61884i	−0.587231	−	0.809419i	$-0.699782\pi$
$53$		−	11.7853i		−	1.61884i	0.587231	−	0.809419i	$-0.300218\pi$
$54$	0.712495			0.0969583
$55$	8.61515	−	4.10661i	1.16167	−	0.553735i
$56$	6.91707			0.924332
$57$			6.72036i			0.890133i
$58$			0.712495i			0.0935552i
$59$	4.46028			0.580679			0.290339	−	0.956924i	$-0.406232\pi$
$59$	4.46028			0.580679			0.290339	+	0.956924i	$0.406232\pi$
$60$	−1.43587	−	3.01228i	−0.185370	−	0.388884i
$61$	−5.24905			−0.672071			−0.336036	−	0.941849i	$-0.609086\pi$
$61$	−5.24905			−0.672071			−0.336036	+	0.941849i	$0.609086\pi$
$62$			6.28464i			0.798150i
$63$		−	2.77986i		−	0.350229i
$64$	−1.73733			−0.217166
$65$	0.750341	+	1.57412i	0.0930684	+	0.195246i
$66$	−3.04103			−0.374325
$67$			8.49375i			1.03768i	0.854872	+	0.518838i	$0.173635\pi$
$67$			8.49375i			1.03768i	−0.854872	+	0.518838i	$0.826365\pi$
$68$			2.84075i			0.344492i
$69$	2.17168			0.261440
$70$	3.99787	−	1.90567i	0.477837	−	0.227772i
$71$	0.663102			0.0786957			0.0393479	−	0.999226i	$-0.487472\pi$
$71$	0.663102			0.0786957			0.0393479	+	0.999226i	$0.487472\pi$
$72$			2.48828i			0.293247i
$73$			16.5345i			1.93522i	0.252455	+	0.967609i	$0.418762\pi$
$73$			16.5345i			1.93522i	−0.252455	+	0.967609i	$0.581238\pi$
$74$	−1.05736			−0.122915
$75$	−3.88418	−	3.14852i	−0.448506	−	0.363560i
$76$	−10.0291			−1.15042
$77$			11.8648i			1.35212i
$78$		−	0.555643i		−	0.0629142i
$79$	−9.54554			−1.07396			−0.536978	−	0.843596i	$-0.680434\pi$
$79$	−9.54554			−1.07396			−0.536978	+	0.843596i	$0.680434\pi$
$80$	2.44602	−	1.16595i	0.273473	−	0.130357i
$81$	1.00000			0.111111
$82$			5.49611i			0.606944i
$83$		−	0.0123998i		−	0.00136106i	−1.00000		0.000680528i	$-0.999783\pi$
$83$		−	0.0123998i		−	0.00136106i	1.00000		0.000680528i	$-0.000216619\pi$
$84$	4.14852			0.452641
$85$	1.83150	+	3.84226i	0.198654	+	0.416752i
$86$	−5.83978			−0.629720
$87$			1.00000i			0.107211i
$88$		−	10.6203i		−	1.13213i
$89$	5.46783			0.579588			0.289794	−	0.957089i	$-0.406413\pi$
$89$	5.46783			0.579588			0.289794	+	0.957089i	$0.406413\pi$
$90$	0.685530	+	1.43816i	0.0722612	+	0.151595i
$91$	−2.16789			−0.227256
$92$			3.24091i			0.337888i
$93$			8.82061i			0.914655i
$94$	3.70056			0.381684
$95$	−13.5649	+	6.46602i	−1.39173	+	0.663399i
$96$	−5.83998			−0.596040
$97$			0.952006i			0.0966615i	0.998831	+	0.0483308i	$0.0153902\pi$
$97$			0.952006i			0.0966615i	−0.998831	+	0.0483308i	$0.984610\pi$
$98$			0.518410i			0.0523673i
$99$	−4.26814			−0.428964
$100$	4.69870	−	5.79655i	0.469870	−	0.579655i
$101$	8.31781			0.827653			0.413826	−	0.910356i	$-0.364192\pi$
$101$	8.31781			0.827653			0.413826	+	0.910356i	$0.364192\pi$
$102$		−	1.35626i		−	0.134290i
$103$			12.4091i			1.22271i	0.791357	+	0.611355i	$0.209375\pi$
$103$			12.4091i			1.22271i	−0.791357	+	0.611355i	$0.790625\pi$
$104$	1.94050			0.190282
$105$	5.61108	−	2.67465i	0.547586	−	0.261019i
$106$	−8.39698			−0.815587
$107$			17.5579i			1.69739i	0.528883	+	0.848695i	$0.322611\pi$
$107$			17.5579i			1.69739i	−0.528883	+	0.848695i	$0.677389\pi$
$108$			1.49235i			0.143602i
$109$	−1.00973			−0.0967146			−0.0483573	−	0.998830i	$-0.515399\pi$
$109$	−1.00973			−0.0967146			−0.0483573	+	0.998830i	$0.515399\pi$
$110$	−2.92594	−	6.13825i	−0.278977	−	0.585259i
$111$	−1.48402			−0.140857
$112$			3.36866i			0.318309i
$113$		−	15.5787i		−	1.46552i	−0.680487	−	0.732761i	$-0.738232\pi$
$113$		−	15.5787i		−	1.46552i	0.680487	−	0.732761i	$-0.261768\pi$
$114$	4.78822			0.448458
$115$	2.08949	+	4.38349i	0.194846	+	0.408763i
$116$	−1.49235			−0.138561
$117$		−	0.779856i		−	0.0720977i
$118$		−	3.17792i		−	0.292552i
$119$	−5.29157			−0.485078
$120$	−5.02255	+	2.39411i	−0.458494	+	0.218551i
$121$	7.21701			0.656091
$122$			3.73992i			0.338596i
$123$			7.71389i			0.695538i
$124$	−13.1634			−1.18211
$125$	2.61805	−	10.8695i	0.234165	−	0.972197i
$126$	−1.98063			−0.176449
$127$			16.9536i			1.50438i	0.658943	+	0.752192i	$0.271004\pi$
$127$			16.9536i			1.50438i	−0.658943	+	0.752192i	$0.728996\pi$
$128$		−	10.4421i		−	0.922961i
$129$	−8.19624			−0.721639
$130$	1.12155	−	0.534614i	0.0983669	−	0.0468888i
$131$	11.9324			1.04254			0.521268	−	0.853393i	$-0.325459\pi$
$131$	11.9324			1.04254			0.521268	+	0.853393i	$0.325459\pi$
$132$		−	6.36956i		−	0.554399i
$133$		−	18.6816i		−	1.61990i
$134$	6.05175			0.522792
$135$	0.962154	+	2.01848i	0.0828090	+	0.173723i
$136$	4.73655			0.406156
$137$			0.239785i			0.0204862i	0.999948	+	0.0102431i	$0.00326054\pi$
$137$			0.239785i			0.0204862i	−0.999948	+	0.0102431i	$0.996739\pi$
$138$		−	1.54731i		−	0.131716i
$139$	17.0255			1.44408			0.722040	−	0.691851i	$-0.243205\pi$
$139$	17.0255			1.44408			0.722040	+	0.691851i	$0.243205\pi$
$140$	3.99151	+	8.37370i	0.337345	+	0.707707i
$141$	5.19381			0.437398
$142$		−	0.472457i		−	0.0396477i
$143$			3.32853i			0.278346i
$144$	−1.21181			−0.100984
$145$	−2.01848	+	0.962154i	−0.167626	+	0.0799025i
$146$	11.7808			0.974982
$147$			0.727598i			0.0600113i
$148$		−	2.21468i		−	0.182045i
$149$	4.13046			0.338380			0.169190	−	0.985583i	$-0.445885\pi$
$149$	4.13046			0.338380			0.169190	+	0.985583i	$0.445885\pi$
$150$	−2.24330	+	2.76746i	−0.183165	+	0.225962i
$151$	−3.21580			−0.261698			−0.130849	−	0.991402i	$-0.541770\pi$
$151$	−3.21580			−0.261698			−0.130849	+	0.991402i	$0.541770\pi$
$152$			16.7221i			1.35635i
$153$		−	1.90354i		−	0.153892i
$154$	8.45362			0.681212
$155$	−17.8042	+	8.48678i	−1.43007	+	0.681675i
$156$	1.16382			0.0931800
$157$		−	6.84237i		−	0.546081i	−0.962003	−	0.273040i	$-0.911971\pi$
$157$		−	6.84237i		−	0.546081i	0.962003	−	0.273040i	$-0.0880292\pi$
$158$			6.80115i			0.541070i
$159$	−11.7853			−0.934637
$160$	−5.61895	−	11.7879i	−0.444217	−	0.931913i
$161$	−6.03696			−0.475779
$162$		−	0.712495i		−	0.0559789i
$163$		−	14.0502i		−	1.10050i	−0.835001	−	0.550248i	$-0.814533\pi$
$163$		−	14.0502i		−	1.10050i	0.835001	−	0.550248i	$-0.185467\pi$
$164$	−11.5118			−0.898923
$165$	−4.10661	−	8.61515i	−0.319699	−	0.670689i
$166$	−0.00883480			−0.000685713
$167$		−	17.8725i		−	1.38301i	−0.722370	−	0.691507i	$-0.756947\pi$
$167$		−	17.8725i		−	1.38301i	0.722370	−	0.691507i	$-0.243053\pi$
$168$		−	6.91707i		−	0.533663i
$169$	12.3918			0.953217
$170$	2.73759	−	1.30494i	0.209964	−	0.100084i
$171$	6.72036			0.513919
$172$		−	12.2317i		−	0.932656i
$173$		−	2.82518i		−	0.214795i	−0.994216	−	0.107397i	$-0.965748\pi$
$173$		−	2.82518i		−	0.214795i	0.994216	−	0.107397i	$-0.0342517\pi$
$174$	0.712495			0.0540141
$175$	10.7974	+	8.75243i	0.816210	+	0.661622i
$176$	5.17218			0.389868
$177$		−	4.46028i		−	0.335255i
$178$		−	3.89580i		−	0.292002i
$179$	−20.2829			−1.51601			−0.758006	−	0.652247i	$-0.773826\pi$
$179$	−20.2829			−1.51601			−0.758006	+	0.652247i	$0.773826\pi$
$180$	−3.01228	+	1.43587i	−0.224522	+	0.107024i
$181$	−8.63783			−0.642045			−0.321023	−	0.947072i	$-0.604027\pi$
$181$	−8.63783			−0.642045			−0.321023	+	0.947072i	$0.604027\pi$
$182$			1.54461i			0.114494i
$183$			5.24905i			0.388021i
$184$	5.40376			0.398370
$185$	−1.42785	−	2.99546i	−0.104978	−	0.220231i
$186$	6.28464			0.460812
$187$			8.12458i			0.594128i
$188$			7.75099i			0.565299i
$189$	−2.77986			−0.202205
$190$	4.60701	+	9.66493i	0.334227	+	0.701168i
$191$	0.896850			0.0648938			0.0324469	−	0.999473i	$-0.489670\pi$
$191$	0.896850			0.0648938			0.0324469	+	0.999473i	$0.489670\pi$
$192$			1.73733i			0.125381i
$193$		−	10.4506i		−	0.752251i	−0.926569	−	0.376126i	$-0.877256\pi$
$193$		−	10.4506i		−	0.752251i	0.926569	−	0.376126i	$-0.122744\pi$
$194$	0.678299			0.0486991
$195$	1.57412	−	0.750341i	0.112725	−	0.0537331i
$196$	−1.08583			−0.0775594
$197$		−	9.57740i		−	0.682361i	−0.939998	−	0.341181i	$-0.889173\pi$
$197$		−	9.57740i		−	0.682361i	0.939998	−	0.341181i	$-0.110827\pi$
$198$			3.04103i			0.216116i
$199$	−5.61768			−0.398227			−0.199113	−	0.979976i	$-0.563806\pi$
$199$	−5.61768			−0.398227			−0.199113	+	0.979976i	$0.563806\pi$
$200$	−9.66493	−	7.83441i	−0.683414	−	0.553976i
$201$	8.49375			0.599103
$202$		−	5.92640i		−	0.416980i
$203$		−	2.77986i		−	0.195108i
$204$	2.84075			0.198892
$205$	−15.5703	+	7.42195i	−1.08748	+	0.518372i
$206$	8.84145			0.616013
$207$		−	2.17168i		−	0.150942i
$208$			0.945039i			0.0655267i
$209$	−28.6834			−1.98407
$210$	−1.90567	−	3.99787i	−0.131504	−	0.275879i
$211$	−0.605216			−0.0416648			−0.0208324	−	0.999783i	$-0.506632\pi$
$211$	−0.605216			−0.0416648			−0.0208324	+	0.999783i	$0.506632\pi$
$212$		−	17.5878i		−	1.20794i
$213$		−	0.663102i		−	0.0454350i
$214$	12.5099			0.855162
$215$	−7.88604	−	16.5439i	−0.537824	−	1.12829i
$216$	2.48828			0.169306
$217$		−	24.5200i		−	1.66453i
$218$			0.719428i			0.0487258i
$219$	16.5345			1.11730
$220$	12.8568	−	6.12850i	0.866807	−	0.413183i
$221$	−1.48449			−0.0998575
$222$			1.05736i			0.0709651i
$223$			16.5537i			1.10852i	0.832344	+	0.554260i	$0.186999\pi$
$223$			16.5537i			1.10852i	−0.832344	+	0.554260i	$0.813001\pi$
$224$	16.2343			1.08470
$225$	−3.14852	+	3.88418i	−0.209901	+	0.258945i
$226$	−11.0997			−0.738344
$227$			22.0061i			1.46060i	0.683128	+	0.730299i	$0.260619\pi$
$227$			22.0061i			1.46060i	−0.683128	+	0.730299i	$0.739381\pi$
$228$			10.0291i			0.664195i
$229$	24.5647			1.62328			0.811641	−	0.584157i	$-0.198575\pi$
$229$	24.5647			1.62328			0.811641	+	0.584157i	$0.198575\pi$
$230$	3.12322	−	1.48875i	0.205939	−	0.0981654i
$231$	11.8648			0.780647
$232$			2.48828i			0.163364i
$233$		−	5.56824i		−	0.364787i	−0.983226	−	0.182394i	$-0.941615\pi$
$233$		−	5.56824i		−	0.364787i	0.983226	−	0.182394i	$-0.0583845\pi$
$234$	−0.555643			−0.0363235
$235$	4.99725	+	10.4836i	0.325984	+	0.683875i
$236$	6.65630			0.433288
$237$			9.54554i			0.620049i
$238$			3.77022i			0.244387i
$239$	−6.90640			−0.446738			−0.223369	−	0.974734i	$-0.571705\pi$
$239$	−6.90640			−0.446738			−0.223369	+	0.974734i	$0.571705\pi$
$240$	−1.16595	−	2.44602i	−0.0752618	−	0.157890i
$241$	−25.1989			−1.62320			−0.811602	−	0.584210i	$-0.801404\pi$
$241$	−25.1989			−1.62320			−0.811602	+	0.584210i	$0.801404\pi$
$242$		−	5.14208i		−	0.330545i
$243$		−	1.00000i		−	0.0641500i
$244$	−7.83342			−0.501483
$245$	−1.46864	+	0.700061i	−0.0938281	+	0.0447253i
$246$	5.49611			0.350419
$247$		−	5.24091i		−	0.333471i
$248$			21.9482i			1.39371i
$249$	−0.0123998			−0.000785805
$250$	−7.74446	−	1.86535i	−0.489803	−	0.117975i
$251$	28.3687			1.79062			0.895309	−	0.445446i	$-0.146955\pi$
$251$	28.3687			1.79062			0.895309	+	0.445446i	$0.146955\pi$
$252$		−	4.14852i		−	0.261332i
$253$			9.26903i			0.582739i
$254$	12.0793			0.757924
$255$	3.84226	−	1.83150i	0.240612	−	0.114693i
$256$	−10.9146			−0.682163
$257$		−	8.71100i		−	0.543377i	−0.962385	−	0.271688i	$-0.912418\pi$
$257$		−	8.71100i		−	0.543377i	0.962385	−	0.271688i	$-0.0875820\pi$
$258$			5.83978i			0.363569i
$259$	4.12536			0.256337
$260$	1.11977	+	2.34914i	0.0694453	+	0.145688i
$261$	1.00000			0.0618984
$262$		−	8.50175i		−	0.525240i
$263$		−	13.2128i		−	0.814736i	−0.913264	−	0.407368i	$-0.866447\pi$
$263$		−	13.2128i		−	0.814736i	0.913264	−	0.407368i	$-0.133553\pi$
$264$	−10.6203			−0.653636
$265$	−11.3393	−	23.7884i	−0.696567	−	1.46131i
$266$	−13.3106			−0.816123
$267$		−	5.46783i		−	0.334625i
$268$			12.6757i			0.774289i
$269$	10.3447			0.630725			0.315363	−	0.948971i	$-0.397874\pi$
$269$	10.3447			0.630725			0.315363	+	0.948971i	$0.397874\pi$
$270$	1.43816	−	0.685530i	0.0875234	−	0.0417200i
$271$	9.76022			0.592891			0.296445	−	0.955050i	$-0.404199\pi$
$271$	9.76022			0.592891			0.296445	+	0.955050i	$0.404199\pi$
$272$			2.30674i			0.139866i
$273$			2.16789i			0.131206i
$274$	0.170845			0.0103212
$275$	13.4383	−	16.5782i	0.810361	−	0.999703i
$276$	3.24091			0.195080
$277$		−	1.87503i		−	0.112659i	−0.998412	−	0.0563297i	$-0.982060\pi$
$277$		−	1.87503i		−	0.112659i	0.998412	−	0.0563297i	$-0.0179398\pi$
$278$		−	12.1306i		−	0.727542i
$279$	8.82061			0.528076
$280$	13.9620	−	6.65528i	0.834387	−	0.397729i
$281$	−21.2930			−1.27024			−0.635118	−	0.772415i	$-0.719049\pi$
$281$	−21.2930			−1.27024			−0.635118	+	0.772415i	$0.719049\pi$
$282$		−	3.70056i		−	0.220365i
$283$		−	15.8729i		−	0.943544i	−0.881721	−	0.471772i	$-0.843615\pi$
$283$		−	15.8729i		−	0.943544i	0.881721	−	0.471772i	$-0.156385\pi$
$284$	0.989581			0.0587208
$285$	6.46602	+	13.5649i	0.383014	+	0.803516i
$286$	2.37156			0.140233
$287$		−	21.4435i		−	1.26577i
$288$			5.83998i			0.344124i
$289$	13.3765			0.786855
$290$	0.685530	+	1.43816i	0.0402557	+	0.0844515i
$291$	0.952006			0.0558076
$292$			24.6753i			1.44401i
$293$		−	33.1369i		−	1.93588i	−0.251189	−	0.967938i	$-0.580822\pi$
$293$		−	33.1369i		−	1.93588i	0.251189	−	0.967938i	$-0.419178\pi$
$294$	0.518410			0.0302343
$295$	9.00298	−	4.29147i	0.524174	−	0.249859i
$296$	−3.69266			−0.214631
$297$			4.26814i			0.247663i
$298$		−	2.94293i		−	0.170479i
$299$	−1.69360			−0.0979433
$300$	−5.79655	−	4.69870i	−0.334664	−	0.271279i
$301$	22.7844			1.31327
$302$			2.29124i			0.131846i
$303$		−	8.31781i		−	0.477845i
$304$	−8.14381			−0.467080
$305$	−10.5951	+	5.05039i	−0.606673	+	0.289184i
$306$	−1.35626			−0.0775325
$307$			17.2605i			0.985109i	0.870282	+	0.492555i	$0.163937\pi$
$307$			17.2605i			0.985109i	−0.870282	+	0.492555i	$0.836063\pi$
$308$			17.7065i			1.00892i
$309$	12.4091			0.705932
$310$	6.04679	+	12.6854i	0.343435	+	0.720483i
$311$	−32.5116			−1.84356			−0.921781	−	0.387711i	$-0.873266\pi$
$311$	−32.5116			−1.84356			−0.921781	+	0.387711i	$0.873266\pi$
$312$		−	1.94050i		−	0.109859i
$313$		−	6.26304i		−	0.354008i	−0.984210	−	0.177004i	$-0.943359\pi$
$313$		−	6.26304i		−	0.354008i	0.984210	−	0.177004i	$-0.0566405\pi$
$314$	−4.87516			−0.275121
$315$	−2.67465	−	5.61108i	−0.150699	−	0.316149i
$316$	−14.2453			−0.801360
$317$		−	18.8523i		−	1.05885i	−0.848356	−	0.529426i	$-0.822407\pi$
$317$		−	18.8523i		−	1.05885i	0.848356	−	0.529426i	$-0.177593\pi$
$318$			8.39698i			0.470879i
$319$	−4.26814			−0.238970
$320$	−3.50676	+	1.67158i	−0.196034	+	0.0934440i
$321$	17.5579			0.979989
$322$			4.30130i			0.239702i
$323$		−	12.7925i		−	0.711793i
$324$	1.49235			0.0829084
$325$	3.02910	+	2.45539i	0.168024	+	0.136201i
$326$	−10.0107			−0.554441
$327$			1.00973i			0.0558382i
$328$			19.1943i			1.05983i
$329$	−14.4380			−0.795995
$330$	−6.13825	+	2.92594i	−0.337900	+	0.161067i
$331$	−0.596245			−0.0327726			−0.0163863	−	0.999866i	$-0.505216\pi$
$331$	−0.596245			−0.0327726			−0.0163863	+	0.999866i	$0.505216\pi$
$332$		−	0.0185049i		−	0.00101559i
$333$			1.48402i			0.0813238i
$334$	−12.7341			−0.696776
$335$	8.17229	+	17.1445i	0.446500	+	0.936702i
$336$	3.36866			0.183776
$337$			32.6414i			1.77809i	0.457818	+	0.889046i	$0.348631\pi$
$337$			32.6414i			1.77809i	−0.457818	+	0.889046i	$0.651369\pi$
$338$		−	8.82911i		−	0.480240i
$339$	−15.5787			−0.846119
$340$	2.73324	+	5.73400i	0.148231	+	0.310970i
$341$	−37.6476			−2.03873
$342$		−	4.78822i		−	0.258917i
$343$			17.4364i			0.941476i
$344$	−20.3946			−1.09960
$345$	4.38349	−	2.08949i	0.235999	−	0.112494i
$346$	−2.01293			−0.108216
$347$		−	13.1985i		−	0.708531i	−0.935145	−	0.354265i	$-0.884731\pi$
$347$		−	13.1985i		−	0.708531i	0.935145	−	0.354265i	$-0.115269\pi$
$348$			1.49235i			0.0799984i
$349$	−15.6412			−0.837255			−0.418628	−	0.908158i	$-0.637489\pi$
$349$	−15.6412			−0.837255			−0.418628	+	0.908158i	$0.637489\pi$
$350$	6.23606	−	7.69313i	0.333332	−	0.411215i
$351$	−0.779856			−0.0416256
$352$		−	24.9258i		−	1.32855i
$353$			5.65486i			0.300978i	0.988612	+	0.150489i	$0.0480848\pi$
$353$			5.65486i			0.300978i	−0.988612	+	0.150489i	$0.951915\pi$
$354$	−3.17792			−0.168905
$355$	1.33846	−	0.638006i	0.0710380	−	0.0338619i
$356$	8.15991			0.432475
$357$			5.29157i			0.280060i
$358$			14.4514i			0.763782i
$359$	−25.2693			−1.33366			−0.666832	−	0.745208i	$-0.732350\pi$
$359$	−25.2693			−1.33366			−0.666832	+	0.745208i	$0.732350\pi$
$360$	2.39411	+	5.02255i	0.126181	+	0.264712i
$361$	26.1632			1.37701
$362$			6.15441i			0.323469i
$363$		−	7.21701i		−	0.378795i
$364$	−3.23525			−0.169573
$365$	15.9087	+	33.3746i	0.832701	+	1.74690i
$366$	3.73992			0.195489
$367$		−	26.2788i		−	1.37174i	−0.727722	−	0.685872i	$-0.759421\pi$
$367$		−	26.2788i		−	1.37174i	0.727722	−	0.685872i	$-0.240579\pi$
$368$			2.63167i			0.137185i
$369$	7.71389			0.401569
$370$	−2.13425	+	1.01734i	−0.110954	+	0.0528890i
$371$	32.7615			1.70089
$372$			13.1634i			0.682493i
$373$			1.43033i			0.0740596i	0.999314	+	0.0370298i	$0.0117897\pi$
$373$			1.43033i			0.0740596i	−0.999314	+	0.0370298i	$0.988210\pi$
$374$	5.78872			0.299328
$375$	−10.8695	−	2.61805i	−0.561298	−	0.135195i
$376$	12.9237			0.666487
$377$		−	0.779856i		−	0.0401646i
$378$			1.98063i			0.101873i
$379$	35.2336			1.80983			0.904915	−	0.425591i	$-0.139934\pi$
$379$	35.2336			1.80983			0.904915	+	0.425591i	$0.139934\pi$
$380$	−20.2436	+	9.64957i	−1.03847	+	0.495012i
$381$	16.9536			0.868557
$382$		−	0.639001i		−	0.0326941i
$383$			32.0701i			1.63870i	0.573291	+	0.819352i	$0.305666\pi$
$383$			32.0701i			1.63870i	−0.573291	+	0.819352i	$0.694334\pi$
$384$	−10.4421			−0.532872
$385$	11.4158	+	23.9489i	0.581802	+	1.22055i
$386$	−7.44601			−0.378992
$387$			8.19624i			0.416638i
$388$			1.42073i			0.0721265i
$389$	−1.63922			−0.0831117			−0.0415558	−	0.999136i	$-0.513231\pi$
$389$	−1.63922			−0.0831117			−0.0415558	+	0.999136i	$0.513231\pi$
$390$	−0.534614	−	1.12155i	−0.0270713	−	0.0567921i
$391$	−4.13389			−0.209060
$392$			1.81047i			0.0914425i
$393$		−	11.9324i		−	0.601908i
$394$	−6.82385			−0.343781
$395$	−19.2675	+	9.18428i	−0.969452	+	0.462111i
$396$	−6.36956			−0.320082
$397$			2.04098i			0.102434i	0.998688	+	0.0512170i	$0.0163100\pi$
$397$			2.04098i			0.102434i	−0.998688	+	0.0512170i	$0.983690\pi$
$398$			4.00257i			0.200631i
$399$	−18.6816			−0.935251
$400$	3.81542	−	4.70689i	0.190771	−	0.235345i
$401$	17.4108			0.869455			0.434727	−	0.900562i	$-0.356845\pi$
$401$	17.4108			0.869455			0.434727	+	0.900562i	$0.356845\pi$
$402$		−	6.05175i		−	0.301834i
$403$		−	6.87880i		−	0.342658i
$404$	12.4131			0.617574
$405$	2.01848	−	0.962154i	0.100299	−	0.0478098i
$406$	−1.98063			−0.0982972
$407$		−	6.33400i		−	0.313965i
$408$		−	4.73655i		−	0.234494i
$409$	37.3010			1.84441			0.922207	−	0.386696i	$-0.126384\pi$
$409$	37.3010			1.84441			0.922207	+	0.386696i	$0.126384\pi$
$410$	5.28810	+	11.0938i	0.261161	+	0.547883i
$411$	0.239785			0.0118277
$412$			18.5188i			0.912356i
$413$			12.3989i			0.610111i
$414$	−1.54731			−0.0760462
$415$	−0.0119305	−	0.0250287i	−0.000585646	−	0.00122861i
$416$	4.55434			0.223295
$417$		−	17.0255i		−	0.833740i
$418$			20.4368i			0.999596i
$419$	−4.32941			−0.211506			−0.105753	−	0.994392i	$-0.533725\pi$
$419$	−4.32941			−0.211506			−0.105753	+	0.994392i	$0.533725\pi$
$420$	8.37370	−	3.99151i	0.408595	−	0.194766i
$421$	−34.2505			−1.66927			−0.834634	−	0.550806i	$-0.814321\pi$
$421$	−34.2505			−1.66927			−0.834634	+	0.550806i	$0.814321\pi$
$422$			0.431214i			0.0209911i
$423$		−	5.19381i		−	0.252532i
$424$	−29.3252			−1.42416
$425$	7.39369	+	5.99334i	0.358647	+	0.290720i
$426$	−0.472457			−0.0228906
$427$		−	14.5916i		−	0.706137i
$428$			26.2026i			1.26655i
$429$	3.32853			0.160703
$430$	−11.7875	+	5.61877i	−0.568443	+	0.270961i
$431$	34.4885			1.66125			0.830626	−	0.556831i	$-0.187983\pi$
$431$	34.4885			1.66125			0.830626	+	0.556831i	$0.187983\pi$
$432$			1.21181i			0.0583034i
$433$		−	3.02258i		−	0.145256i	−0.997359	−	0.0726279i	$-0.976861\pi$
$433$		−	3.02258i		−	0.145256i	0.997359	−	0.0726279i	$-0.0231386\pi$
$434$	−17.4704			−0.838606
$435$	0.962154	+	2.01848i	0.0461317	+	0.0967787i
$436$	−1.50687			−0.0721661
$437$		−	14.5945i		−	0.698148i
$438$		−	11.7808i		−	0.562906i
$439$	−8.37392			−0.399665			−0.199833	−	0.979830i	$-0.564040\pi$
$439$	−8.37392			−0.399665			−0.199833	+	0.979830i	$0.564040\pi$
$440$	−10.2184	−	21.4369i	−0.487143	−	1.02197i
$441$	0.727598			0.0346475
$442$			1.05769i			0.0503092i
$443$			29.8770i			1.41950i	0.704454	+	0.709749i	$0.251192\pi$
$443$			29.8770i			1.41950i	−0.704454	+	0.709749i	$0.748808\pi$
$444$	−2.21468			−0.105104
$445$	11.0367	−	5.26089i	0.523189	−	0.249390i
$446$	11.7945			0.558484
$447$		−	4.13046i		−	0.195364i
$448$		−	4.82952i		−	0.228174i
$449$	−12.0780			−0.569994			−0.284997	−	0.958528i	$-0.591993\pi$
$449$	−12.0780			−0.569994			−0.284997	+	0.958528i	$0.591993\pi$
$450$	2.76746	+	2.24330i	0.130459	+	0.105750i
$451$	−32.9240			−1.55033
$452$		−	23.2489i		−	1.09354i
$453$			3.21580i			0.151092i
$454$	15.6793			0.735864
$455$	−4.37583	+	2.08584i	−0.205142	+	0.0977857i
$456$	16.7221			0.783086
$457$			3.03357i			0.141905i	0.997480	+	0.0709523i	$0.0226038\pi$
$457$			3.03357i			0.141905i	−0.997480	+	0.0709523i	$0.977396\pi$
$458$		−	17.5022i		−	0.817826i
$459$	−1.90354			−0.0888497
$460$	3.11825	+	6.54171i	0.145389	+	0.305009i
$461$	−4.44508			−0.207028			−0.103514	−	0.994628i	$-0.533009\pi$
$461$	−4.44508			−0.207028			−0.103514	+	0.994628i	$0.533009\pi$
$462$		−	8.45362i		−	0.393298i
$463$			9.04875i			0.420531i	0.977644	+	0.210266i	$0.0674329\pi$
$463$			9.04875i			0.420531i	−0.977644	+	0.210266i	$0.932567\pi$
$464$	−1.21181			−0.0562570
$465$	8.48678	+	17.8042i	0.393565	+	0.825651i
$466$	−3.96734			−0.183784
$467$			8.11327i			0.375437i	0.982223	+	0.187719i	$0.0601093\pi$
$467$			8.11327i			0.375437i	−0.982223	+	0.187719i	$0.939891\pi$
$468$		−	1.16382i		−	0.0537975i
$469$	−23.6114			−1.09027
$470$	7.46951	−	3.56051i	0.344543	−	0.164234i
$471$	−6.84237			−0.315280
$472$		−	11.0984i		−	0.510847i
$473$		−	34.9827i		−	1.60851i
$474$	6.80115			0.312387
$475$	−21.1592	+	26.1030i	−0.970850	+	1.19769i
$476$	−7.89688			−0.361953
$477$			11.7853i			0.539613i
$478$			4.92078i			0.225071i
$479$	−6.62947			−0.302908			−0.151454	−	0.988464i	$-0.548396\pi$
$479$	−6.62947			−0.302908			−0.151454	+	0.988464i	$0.548396\pi$
$480$	−11.7879	+	5.61895i	−0.538040	+	0.256469i
$481$	1.15732			0.0527693
$482$			17.9541i			0.817787i
$483$			6.03696i			0.274691i
$484$	10.7703			0.489559
$485$	0.915976	+	1.92160i	0.0415923	+	0.0872556i
$486$	−0.712495			−0.0323194
$487$		−	29.2047i		−	1.32339i	−0.749773	−	0.661695i	$-0.769837\pi$
$487$		−	29.2047i		−	1.32339i	0.749773	−	0.661695i	$-0.230163\pi$
$488$			13.0611i			0.591249i
$489$	−14.0502			−0.635372
$490$	0.498790	+	1.04640i	0.0225330	+	0.0472715i
$491$	−4.32464			−0.195168			−0.0975841	−	0.995227i	$-0.531111\pi$
$491$	−4.32464			−0.195168			−0.0975841	+	0.995227i	$0.531111\pi$
$492$			11.5118i			0.518994i
$493$		−	1.90354i		−	0.0857312i
$494$	−3.73412			−0.168006
$495$	−8.61515	+	4.10661i	−0.387222	+	0.184578i
$496$	−10.6889			−0.479947
$497$			1.84333i			0.0826846i
$498$			0.00883480i			0.000395897i
$499$	−4.29688			−0.192355			−0.0961774	−	0.995364i	$-0.530662\pi$
$499$	−4.29688			−0.192355			−0.0961774	+	0.995364i	$0.530662\pi$
$500$	3.90705	−	16.2211i	0.174728	−	0.725429i
$501$	−17.8725			−0.798483
$502$		−	20.2126i		−	0.902131i
$503$			14.2512i			0.635429i	0.948186	+	0.317715i	$0.102915\pi$
$503$			14.2512i			0.635429i	−0.948186	+	0.317715i	$0.897085\pi$
$504$	−6.91707			−0.308111
$505$	16.7893	−	8.00301i	0.747115	−	0.356129i
$506$	6.60414			0.293590
$507$		−	12.3918i		−	0.550340i
$508$			25.3007i			1.12254i
$509$	19.4974			0.864206			0.432103	−	0.901824i	$-0.357772\pi$
$509$	19.4974			0.864206			0.432103	+	0.901824i	$0.357772\pi$
$510$	−1.30494	−	2.73759i	−0.0577835	−	0.121223i
$511$	−45.9635			−2.03331
$512$		−	13.1076i		−	0.579280i
$513$		−	6.72036i		−	0.296711i
$514$	−6.20654			−0.273759
$515$	11.9395	+	25.0476i	0.526117	+	1.10373i
$516$	−12.2317			−0.538469
$517$			22.1679i			0.974943i
$518$		−	2.93930i		−	0.129145i
$519$	−2.82518			−0.124012
$520$	3.91686	−	1.86706i	0.171766	−	0.0818760i
$521$	24.5229			1.07437			0.537185	−	0.843465i	$-0.319488\pi$
$521$	24.5229			1.07437			0.537185	+	0.843465i	$0.319488\pi$
$522$		−	0.712495i		−	0.0311851i
$523$			10.8566i			0.474725i	0.971421	+	0.237362i	$0.0762829\pi$
$523$			10.8566i			0.474725i	−0.971421	+	0.237362i	$0.923717\pi$
$524$	17.8073			0.777914
$525$	8.75243	−	10.7974i	0.381987	−	0.471239i
$526$	−9.41406			−0.410472
$527$		−	16.7904i		−	0.731401i
$528$		−	5.17218i		−	0.225090i
$529$	18.2838			0.794948
$530$	−16.9491	+	8.07919i	−0.736224	+	0.350938i
$531$	−4.46028			−0.193560
$532$		−	27.8795i		−	1.20873i
$533$		−	6.01572i		−	0.260570i
$534$	−3.89580			−0.168588
$535$	16.8934	+	35.4403i	0.730367	+	1.53222i
$536$	21.1348			0.912886
$537$			20.2829i			0.875270i
$538$		−	7.37052i		−	0.317766i
$539$	−3.10549			−0.133763
$540$	1.43587	+	3.01228i	0.0617901	+	0.129628i
$541$	−22.7032			−0.976085			−0.488043	−	0.872820i	$-0.662289\pi$
$541$	−22.7032			−0.976085			−0.488043	+	0.872820i	$0.662289\pi$
$542$		−	6.95410i		−	0.298704i
$543$			8.63783i			0.370685i
$544$	11.1166			0.476622
$545$	−2.03812	+	0.971516i	−0.0873035	+	0.0416152i
$546$	1.54461			0.0661031
$547$		−	32.8229i		−	1.40340i	−0.712471	−	0.701702i	$-0.752424\pi$
$547$		−	32.8229i		−	1.40340i	0.712471	−	0.701702i	$-0.247576\pi$
$548$			0.357843i			0.0152863i
$549$	5.24905			0.224024
$550$	−11.8119	−	9.57474i	−0.503660	−	0.408268i
$551$	6.72036			0.286297
$552$		−	5.40376i		−	0.229999i
$553$		−	26.5352i		−	1.12839i
$554$	−1.33595			−0.0567590
$555$	−2.99546	+	1.42785i	−0.127150	+	0.0606091i
$556$	25.4080			1.07754
$557$			26.3234i			1.11536i	0.830057	+	0.557679i	$0.188308\pi$
$557$			26.3234i			1.11536i	−0.830057	+	0.557679i	$0.811692\pi$
$558$		−	6.28464i		−	0.266050i
$559$	6.39189			0.270348
$560$	3.24117	+	6.79958i	0.136965	+	0.287335i
$561$	8.12458			0.343020
$562$			15.1712i			0.639958i
$563$		−	28.4750i		−	1.20008i	−0.799971	−	0.600039i	$-0.795152\pi$
$563$		−	28.4750i		−	1.20008i	0.799971	−	0.600039i	$-0.204848\pi$
$564$	7.75099			0.326375
$565$	−14.9891	−	31.4453i	−0.630597	−	1.32291i
$566$	−11.3093			−0.475367
$567$			2.77986i			0.116743i
$568$		−	1.64999i		−	0.0692318i
$569$	14.7555			0.618582			0.309291	−	0.950967i	$-0.399908\pi$
$569$	14.7555			0.618582			0.309291	+	0.950967i	$0.399908\pi$
$570$	9.66493	−	4.60701i	0.404819	−	0.192966i
$571$	−0.204397			−0.00855376			−0.00427688	−	0.999991i	$-0.501361\pi$
$571$	−0.204397			−0.00855376			−0.00427688	+	0.999991i	$0.501361\pi$
$572$			4.96734i			0.207695i
$573$		−	0.896850i		−	0.0374664i
$574$	−15.2784			−0.637708
$575$	8.43519	+	6.83758i	0.351772	+	0.285147i
$576$	1.73733			0.0723887
$577$		−	37.3300i		−	1.55407i	−0.629457	−	0.777035i	$-0.716723\pi$
$577$		−	37.3300i		−	1.55407i	0.629457	−	0.777035i	$-0.283277\pi$
$578$		−	9.53071i		−	0.396425i
$579$	−10.4506			−0.434312
$580$	−3.01228	+	1.43587i	−0.125078	+	0.0596213i
$581$	0.0344697			0.00143004
$582$		−	0.678299i		−	0.0281164i
$583$		−	50.3014i		−	2.08327i
$584$	41.1425			1.70249
$585$	−0.750341	−	1.57412i	−0.0310228	−	0.0650820i
$586$	−23.6098			−0.975314
$587$		−	10.8497i		−	0.447813i	−0.974611	−	0.223907i	$-0.928119\pi$
$587$		−	10.8497i		−	0.447813i	0.974611	−	0.223907i	$-0.0718811\pi$
$588$			1.08583i			0.0447789i
$589$	59.2776			2.44249
$590$	−3.05765	−	6.41458i	−0.125882	−	0.264084i
$591$	−9.57740			−0.393962
$592$		−	1.79835i		−	0.0739119i
$593$		−	14.0575i		−	0.577272i	−0.957439	−	0.288636i	$-0.906798\pi$
$593$		−	14.0575i		−	0.577272i	0.957439	−	0.288636i	$-0.0932018\pi$
$594$	3.04103			0.124775
$595$	−10.6809	+	5.09131i	−0.437876	+	0.208723i
$596$	6.16409			0.252491
$597$			5.61768i			0.229916i
$598$			1.20668i			0.0493448i
$599$	5.52446			0.225724			0.112862	−	0.993611i	$-0.463998\pi$
$599$	5.52446			0.225724			0.112862	+	0.993611i	$0.463998\pi$
$600$	−7.83441	+	9.66493i	−0.319838	+	0.394569i
$601$	−6.85394			−0.279578			−0.139789	−	0.990181i	$-0.544642\pi$
$601$	−6.85394			−0.279578			−0.139789	+	0.990181i	$0.544642\pi$
$602$		−	16.2337i		−	0.661638i
$603$		−	8.49375i		−	0.345892i
$604$	−4.79910			−0.195273
$605$	14.5674	−	6.94387i	0.592248	−	0.282308i
$606$	−5.92640			−0.240743
$607$			30.4979i			1.23787i	0.785442	+	0.618935i	$0.212436\pi$
$607$			30.4979i			1.23787i	−0.785442	+	0.618935i	$0.787564\pi$
$608$			39.2467i			1.59166i
$609$	−2.77986			−0.112645
$610$	3.59838	+	7.54895i	0.145694	+	0.305648i
$611$	−4.05042			−0.163863
$612$		−	2.84075i		−	0.114831i
$613$		−	29.9211i		−	1.20850i	−0.796794	−	0.604250i	$-0.793473\pi$
$613$		−	29.9211i		−	1.20850i	0.796794	−	0.604250i	$-0.206527\pi$
$614$	12.2980			0.496308
$615$	7.42195	+	15.5703i	0.299282	+	0.627857i
$616$	29.5230			1.18952
$617$		−	1.04305i		−	0.0419917i	−0.999780	−	0.0209959i	$-0.993316\pi$
$617$		−	1.04305i		−	0.0419917i	0.999780	−	0.0209959i	$-0.00668368\pi$
$618$		−	8.84145i		−	0.355655i
$619$	−22.1661			−0.890930			−0.445465	−	0.895299i	$-0.646962\pi$
$619$	−22.1661			−0.890930			−0.445465	+	0.895299i	$0.646962\pi$
$620$	−26.5701	+	12.6653i	−1.06708	+	0.508649i
$621$	−2.17168			−0.0871465
$622$			23.1643i			0.928805i
$623$			15.1998i			0.608966i
$624$	0.945039			0.0378318
$625$	−5.17364	−	24.4588i	−0.206946	−	0.978352i
$626$	−4.46238			−0.178353
$627$			28.6834i			1.14551i
$628$		−	10.2112i		−	0.407472i
$629$	2.82489			0.112636
$630$	−3.99787	+	1.90567i	−0.159279	+	0.0759239i
$631$	20.1089			0.800524			0.400262	−	0.916401i	$-0.368919\pi$
$631$	20.1089			0.800524			0.400262	+	0.916401i	$0.368919\pi$
$632$			23.7520i			0.944804i
$633$			0.605216i			0.0240552i
$634$	−13.4322			−0.533460
$635$	16.3119	+	34.2204i	0.647319	+	1.35800i
$636$	−17.5878			−0.697403
$637$		−	0.567422i		−	0.0224821i
$638$			3.04103i			0.120395i
$639$	−0.663102			−0.0262319
$640$	−10.0469	−	21.0772i	−0.397139	−	0.833149i
$641$	5.93422			0.234388			0.117194	−	0.993109i	$-0.462610\pi$
$641$	5.93422			0.234388			0.117194	+	0.993109i	$0.462610\pi$
$642$		−	12.5099i		−	0.493728i
$643$		−	0.951317i		−	0.0375163i	−0.999824	−	0.0187581i	$-0.994029\pi$
$643$		−	0.951317i		−	0.0375163i	0.999824	−	0.0187581i	$-0.00597125\pi$
$644$	−9.00926			−0.355015
$645$	−16.5439	+	7.88604i	−0.651417	+	0.310513i
$646$	−9.11458			−0.358608
$647$		−	35.1384i		−	1.38143i	−0.723126	−	0.690716i	$-0.757295\pi$
$647$		−	35.1384i		−	1.38143i	0.723126	−	0.690716i	$-0.242705\pi$
$648$		−	2.48828i		−	0.0977490i
$649$	19.0371			0.747271
$650$	1.74945	−	2.15822i	0.0686192	−	0.0846522i
$651$	−24.5200			−0.961015
$652$		−	20.9678i		−	0.821163i
$653$			45.9930i			1.79984i	0.436050	+	0.899922i	$0.356377\pi$
$653$			45.9930i			1.79984i	−0.436050	+	0.899922i	$0.643623\pi$
$654$	0.719428			0.0281319
$655$	24.0852	−	11.4808i	0.941088	−	0.448591i
$656$	−9.34779			−0.364970
$657$		−	16.5345i		−	0.645072i
$658$			10.2870i			0.401030i
$659$	19.3162			0.752451			0.376226	−	0.926528i	$-0.377222\pi$
$659$	19.3162			0.752451			0.376226	+	0.926528i	$0.377222\pi$
$660$	−6.12850	−	12.8568i	−0.238551	−	0.500451i
$661$	44.3224			1.72394			0.861970	−	0.506959i	$-0.169230\pi$
$661$	44.3224			1.72394			0.861970	+	0.506959i	$0.169230\pi$
$662$			0.424821i			0.0165111i
$663$			1.48449i			0.0576528i
$664$	−0.0308542			−0.00119738
$665$	−17.9746	−	37.7085i	−0.697025	−	1.46227i
$666$	1.05736			0.0409717
$667$		−	2.17168i		−	0.0840878i
$668$		−	26.6720i		−	1.03197i
$669$	16.5537			0.640004
$670$	12.2153	−	5.82272i	0.471920	−	0.224951i
$671$	−22.4037			−0.864883
$672$		−	16.2343i		−	0.626251i
$673$		−	12.7421i		−	0.491170i	−0.969375	−	0.245585i	$-0.921020\pi$
$673$		−	12.7421i		−	0.491170i	0.969375	−	0.245585i	$-0.0789801\pi$
$674$	23.2569			0.895821
$675$	3.88418	+	3.14852i	0.149502	+	0.121187i
$676$	18.4930			0.711267
$677$		−	9.41654i		−	0.361907i	−0.983492	−	0.180954i	$-0.942082\pi$
$677$		−	9.41654i		−	0.361907i	0.983492	−	0.180954i	$-0.0579184\pi$
$678$			11.0997i			0.426283i
$679$	−2.64644			−0.101561
$680$	9.56063	−	4.55729i	0.366634	−	0.174764i
$681$	22.0061			0.843276
$682$			26.8237i			1.02713i
$683$		−	6.92316i		−	0.264907i	−0.991189	−	0.132454i	$-0.957714\pi$
$683$		−	6.92316i		−	0.264907i	0.991189	−	0.132454i	$-0.0422856\pi$
$684$	10.0291			0.383473
$685$	0.230710	+	0.484001i	0.00881497	+	0.0184927i
$686$	12.4233			0.474325
$687$		−	24.5647i		−	0.937202i
$688$		−	9.93231i		−	0.378666i
$689$	9.19085			0.350144
$690$	−1.48875	−	3.12322i	−0.0566758	−	0.118899i
$691$	−48.7272			−1.85367			−0.926835	−	0.375469i	$-0.877482\pi$
$691$	−48.7272			−1.85367			−0.926835	+	0.375469i	$0.877482\pi$
$692$		−	4.21616i		−	0.160274i
$693$		−	11.8648i		−	0.450707i
$694$	−9.40384			−0.356965
$695$	34.3655	−	16.3811i	1.30356	−	0.621371i
$696$	2.48828			0.0943181
$697$		−	14.6837i		−	0.556186i
$698$			11.1443i			0.421818i
$699$	−5.56824			−0.210610
$700$	16.1136	+	13.0617i	0.609036	+	0.493686i
$701$	2.88580			0.108995			0.0544975	−	0.998514i	$-0.482644\pi$
$701$	2.88580			0.108995			0.0544975	+	0.998514i	$0.482644\pi$
$702$			0.555643i			0.0209714i
$703$			9.97314i			0.376144i
$704$	−7.41516			−0.279469
$705$	10.4836	−	4.99725i	0.394835	−	0.188207i
$706$	4.02906			0.151636
$707$			23.1223i			0.869604i
$708$		−	6.65630i		−	0.250159i
$709$	1.73056			0.0649924			0.0324962	−	0.999472i	$-0.489654\pi$
$709$	1.73056			0.0649924			0.0324962	+	0.999472i	$0.489654\pi$
$710$	−0.454576	−	0.953645i	−0.0170599	−	0.0357896i
$711$	9.54554			0.357986
$712$		−	13.6055i		−	0.509887i
$713$		−	19.1555i		−	0.717381i
$714$	3.77022			0.141097
$715$	3.20256	+	6.71857i	0.119769	+	0.251260i
$716$	−30.2692			−1.13121
$717$			6.90640i			0.257924i
$718$			18.0043i			0.671913i
$719$	12.9089			0.481420			0.240710	−	0.970597i	$-0.422620\pi$
$719$	12.9089			0.481420			0.240710	+	0.970597i	$0.422620\pi$
$720$	−2.44602	+	1.16595i	−0.0911577	+	0.0434524i
$721$	−34.4956			−1.28468
$722$		−	18.6412i		−	0.693752i
$723$			25.1989i			0.937158i
$724$	−12.8907			−0.479078
$725$	−3.14852	+	3.88418i	−0.116933	+	0.144255i
$726$	−5.14208			−0.190841
$727$		−	38.3405i		−	1.42197i	−0.703207	−	0.710985i	$-0.748249\pi$
$727$		−	38.3405i		−	1.42197i	0.703207	−	0.710985i	$-0.251751\pi$
$728$			5.39431i			0.199927i
$729$	−1.00000			−0.0370370
$730$	23.7792	−	11.3349i	0.880108	−	0.419523i
$731$	15.6019			0.577057
$732$			7.83342i			0.289531i
$733$			34.8966i			1.28894i	0.764631	+	0.644468i	$0.222921\pi$
$733$			34.8966i			1.28894i	−0.764631	+	0.644468i	$0.777079\pi$
$734$	−18.7235			−0.691098
$735$	0.700061	+	1.46864i	0.0258222	+	0.0541717i
$736$	12.6826			0.467485
$737$			36.2525i			1.33538i
$738$		−	5.49611i		−	0.202315i
$739$	−14.2969			−0.525921			−0.262960	−	0.964807i	$-0.584699\pi$
$739$	−14.2969			−0.525921			−0.262960	+	0.964807i	$0.584699\pi$
$740$	−2.13086	−	4.47028i	−0.0783320	−	0.164331i
$741$	−5.24091			−0.192530
$742$		−	23.3424i		−	0.856927i
$743$			44.1357i			1.61918i	0.586995	+	0.809591i	$0.300311\pi$
$743$			44.1357i			1.61918i	−0.586995	+	0.809591i	$0.699689\pi$
$744$	21.9482			0.804659
$745$	8.33725	−	3.97414i	0.305453	−	0.145601i
$746$	1.01910			0.0373120
$747$			0.0123998i			0.000453685i
$748$			12.1247i			0.443324i
$749$	−48.8085			−1.78343
$750$	−1.86535	+	7.74446i	−0.0681128	+	0.282788i
$751$	9.56375			0.348986			0.174493	−	0.984658i	$-0.444171\pi$
$751$	9.56375			0.348986			0.174493	+	0.984658i	$0.444171\pi$
$752$			6.29393i			0.229516i
$753$		−	28.3687i		−	1.03381i
$754$	−0.555643			−0.0202353
$755$	−6.49103	+	3.09410i	−0.236233	+	0.112606i
$756$	−4.14852			−0.150880
$757$			30.1910i			1.09731i	0.836048	+	0.548656i	$0.184860\pi$
$757$			30.1910i			1.09731i	−0.836048	+	0.548656i	$0.815140\pi$
$758$		−	25.1038i		−	0.911811i
$759$	9.26903			0.336445
$760$	16.0893	+	33.7533i	0.583619	+	1.22436i
$761$	8.27038			0.299801			0.149900	−	0.988701i	$-0.452105\pi$
$761$	8.27038			0.299801			0.149900	+	0.988701i	$0.452105\pi$
$762$		−	12.0793i		−	0.437588i
$763$		−	2.80690i		−	0.101617i
$764$	1.33841			0.0484221
$765$	−1.83150	−	3.84226i	−0.0662180	−	0.138917i
$766$	22.8498			0.825595
$767$			3.47837i			0.125597i
$768$			10.9146i			0.393847i
$769$	22.4592			0.809901			0.404950	−	0.914339i	$-0.367289\pi$
$769$	22.4592			0.809901			0.404950	+	0.914339i	$0.367289\pi$
$770$	17.0635	−	8.13368i	0.614924	−	0.293118i
$771$	−8.71100			−0.313719
$772$		−	15.5960i		−	0.561311i
$773$			26.9520i			0.969398i	0.874681	+	0.484699i	$0.161071\pi$
$773$			26.9520i			0.969398i	−0.874681	+	0.484699i	$0.838929\pi$
$774$	5.83978			0.209907
$775$	−27.7719	+	34.2608i	−0.997595	+	1.23068i
$776$	2.36886			0.0850371
$777$		−	4.12536i		−	0.147996i
$778$			1.16794i			0.0418725i
$779$	51.8401			1.85737
$780$	2.34914	−	1.11977i	0.0841128	−	0.0400943i
$781$	2.83021			0.101273
$782$			2.94537i			0.105326i
$783$		−	1.00000i		−	0.0357371i
$784$	−0.881713			−0.0314897
$785$	−6.58341	−	13.8112i	−0.234972	−	0.492942i
$786$	−8.50175			−0.303247
$787$			1.16423i			0.0415004i	0.999785	+	0.0207502i	$0.00660546\pi$
$787$			1.16423i			0.0415004i	−0.999785	+	0.0207502i	$0.993395\pi$
$788$		−	14.2928i		−	0.509161i
$789$	−13.2128			−0.470388
$790$	6.54375	+	13.7280i	0.232816	+	0.488420i
$791$	43.3065			1.53980
$792$			10.6203i			0.377377i
$793$		−	4.09350i		−	0.145364i
$794$	1.45419			0.0516073
$795$	−23.7884	+	11.3393i	−0.843689	+	0.402163i
$796$	−8.38354			−0.297147
$797$			15.9624i			0.565418i	0.959206	+	0.282709i	$0.0912331\pi$
$797$			15.9624i			0.565418i	−0.959206	+	0.282709i	$0.908767\pi$
$798$			13.3106i			0.471189i
$799$	−9.88664			−0.349764
$800$	−22.6835	−	18.3873i	−0.801983	−	0.650089i
$801$	−5.46783			−0.193196
$802$		−	12.4051i		−	0.438040i
$803$			70.5715i			2.49042i
$804$	12.6757			0.447036
$805$	−12.1855	+	5.80848i	−0.429482	+	0.204722i
$806$	−4.90111			−0.172634
$807$		−	10.3447i		−	0.364149i
$808$		−	20.6971i		−	0.728120i
$809$	7.83605			0.275501			0.137750	−	0.990467i	$-0.456013\pi$
$809$	7.83605			0.275501			0.137750	+	0.990467i	$0.456013\pi$
$810$	−0.685530	−	1.43816i	−0.0240871	−	0.0505317i
$811$	−23.9935			−0.842526			−0.421263	−	0.906939i	$-0.638413\pi$
$811$	−23.9935			−0.842526			−0.421263	+	0.906939i	$0.638413\pi$
$812$		−	4.14852i		−	0.145585i
$813$		−	9.76022i		−	0.342306i
$814$	−4.51294			−0.158179
$815$	−13.5184	−	28.3600i	−0.473531	−	0.993409i
$816$	2.30674			0.0807519
$817$			55.0817i			1.92706i
$818$		−	26.5768i		−	0.929235i
$819$	2.16789			0.0757521
$820$	−23.2364	+	11.0762i	−0.811450	+	0.386796i
$821$	−12.8804			−0.449528			−0.224764	−	0.974413i	$-0.572161\pi$
$821$	−12.8804			−0.449528			−0.224764	+	0.974413i	$0.572161\pi$
$822$		−	0.170845i		−	0.00595892i
$823$		−	47.8165i		−	1.66678i	−0.552687	−	0.833389i	$-0.686397\pi$
$823$		−	47.8165i		−	1.66678i	0.552687	−	0.833389i	$-0.313603\pi$
$824$	30.8775			1.07567
$825$	−16.5782	−	13.4383i	−0.577179	−	0.467862i
$826$	8.83417			0.307380
$827$		−	14.6873i		−	0.510726i	−0.966845	−	0.255363i	$-0.917805\pi$
$827$		−	14.6873i		−	0.510726i	0.966845	−	0.255363i	$-0.0821951\pi$
$828$		−	3.24091i		−	0.112629i
$829$	−41.9876			−1.45829			−0.729145	−	0.684359i	$-0.760082\pi$
$829$	−41.9876			−1.45829			−0.729145	+	0.684359i	$0.760082\pi$
$830$	−0.0178329	+	0.00850043i	−0.000618988	+	0.000295054i
$831$	−1.87503			−0.0650440
$832$		−	1.35487i		−	0.0469715i
$833$		−	1.38501i		−	0.0479879i
$834$	−12.1306			−0.420047
$835$	−17.1961	−	36.0752i	−0.595095	−	1.24843i
$836$	−42.8057			−1.48047
$837$		−	8.82061i		−	0.304885i
$838$			3.08468i			0.106559i
$839$	4.04408			0.139617			0.0698085	−	0.997560i	$-0.477761\pi$
$839$	4.04408			0.139617			0.0698085	+	0.997560i	$0.477761\pi$
$840$	−6.65528	−	13.9620i	−0.229629	−	0.481733i
$841$	1.00000			0.0344828
$842$			24.4033i			0.840994i
$843$			21.2930i			0.733371i
$844$	−0.903195			−0.0310892
$845$	25.0126	−	11.9228i	0.860461	−	0.410158i
$846$	−3.70056			−0.127228
$847$			20.0622i			0.689347i
$848$		−	14.2816i		−	0.490432i
$849$	−15.8729			−0.544755
$850$	4.27023	−	5.26797i	0.146468	−	0.180690i
$851$	3.22282			0.110477
$852$		−	0.989581i		−	0.0339025i
$853$			43.8299i			1.50071i	0.661037	+	0.750353i	$0.270117\pi$
$853$			43.8299i			1.50071i	−0.661037	+	0.750353i	$0.729883\pi$
$854$	−10.3964			−0.355759
$855$	13.5649	−	6.46602i	0.463910	−	0.221133i
$856$	43.6891			1.49326
$857$			2.09275i			0.0714868i	0.999361	+	0.0357434i	$0.0113799\pi$
$857$			2.09275i			0.0714868i	−0.999361	+	0.0357434i	$0.988620\pi$
$858$		−	2.37156i		−	0.0809638i
$859$	−46.5885			−1.58958			−0.794790	−	0.606885i	$-0.792419\pi$
$859$	−46.5885			−1.58958			−0.794790	+	0.606885i	$0.792419\pi$
$860$	−11.7687	−	24.6894i	−0.401311	−	0.841900i
$861$	−21.4435			−0.730793
$862$		−	24.5729i		−	0.836955i
$863$		−	32.1466i		−	1.09428i	−0.837040	−	0.547141i	$-0.815716\pi$
$863$		−	32.1466i		−	1.09428i	0.837040	−	0.547141i	$-0.184284\pi$
$864$	5.83998			0.198680
$865$	−2.71826	−	5.70257i	−0.0924236	−	0.193893i
$866$	−2.15357			−0.0731814
$867$		−	13.3765i		−	0.454291i
$868$		−	36.5925i		−	1.24203i
$869$	−40.7417			−1.38207
$870$	1.43816	−	0.685530i	0.0487581	−	0.0232416i
$871$	−6.62390			−0.224442
$872$			2.51249i			0.0850838i
$873$		−	0.952006i		−	0.0322205i
$874$	−10.3985			−0.351734
$875$	30.2156	+	7.27780i	1.02147	+	0.246035i
$876$	24.6753			0.833700
$877$			48.0544i			1.62268i	0.584572	+	0.811342i	$0.301262\pi$
$877$			48.0544i			1.62268i	−0.584572	+	0.811342i	$0.698738\pi$
$878$			5.96637i			0.201355i
$879$	−33.1369			−1.11768
$880$	10.4399	−	4.97644i	0.351931	−	0.167756i
$881$	−30.9846			−1.04390			−0.521950	−	0.852976i	$-0.674795\pi$
$881$	−30.9846			−1.04390			−0.521950	+	0.852976i	$0.674795\pi$
$882$		−	0.518410i		−	0.0174558i
$883$		−	9.60378i		−	0.323193i	−0.986857	−	0.161597i	$-0.948336\pi$
$883$		−	9.60378i		−	0.323193i	0.986857	−	0.161597i	$-0.0516643\pi$
$884$	−2.21538			−0.0745112
$885$	−4.29147	−	9.00298i	−0.144256	−	0.302632i
$886$	21.2872			0.715158
$887$		−	29.7279i		−	0.998165i	−0.866554	−	0.499083i	$-0.833670\pi$
$887$		−	29.7279i		−	0.998165i	0.866554	−	0.499083i	$-0.166330\pi$
$888$			3.69266i			0.123918i
$889$	−47.1284			−1.58064
$890$	−3.74836	−	7.86359i	−0.125645	−	0.263588i
$891$	4.26814			0.142988
$892$			24.7040i			0.827150i
$893$		−	34.9043i		−	1.16803i
$894$	−2.94293			−0.0984263
$895$	−40.9406	+	19.5152i	−1.36849	+	0.652322i
$896$	29.0276			0.969743
$897$			1.69360i			0.0565476i
$898$			8.60548i			0.287169i
$899$	8.82061			0.294184
$900$	−4.69870	+	5.79655i	−0.156623	+	0.193218i
$901$	22.4339			0.747380
$902$			23.4582i			0.781071i
$903$		−	22.7844i		−	0.758216i
$904$	−38.7642			−1.28928
$905$	−17.4353	+	8.31092i	−0.579569	+	0.276264i
$906$	2.29124			0.0761214
$907$			4.35876i			0.144730i	0.997378	+	0.0723651i	$0.0230547\pi$
$907$			4.35876i			0.144730i	−0.997378	+	0.0723651i	$0.976945\pi$
$908$			32.8409i			1.08986i
$909$	−8.31781			−0.275884
$910$	1.48615	+	3.11776i	0.0492654	+	0.103353i
$911$	−0.389317			−0.0128986			−0.00644932	−	0.999979i	$-0.502053\pi$
$911$	−0.389317			−0.0128986			−0.00644932	+	0.999979i	$0.502053\pi$
$912$			8.14381i			0.269669i
$913$		−	0.0529241i		−	0.00175153i
$914$	2.16141			0.0714930
$915$	5.05039	+	10.5951i	0.166961	+	0.350263i
$916$	36.6592			1.21125
$917$			33.1703i			1.09538i
$918$			1.35626i			0.0447634i
$919$	54.9915			1.81400			0.907001	−	0.421128i	$-0.138366\pi$
$919$	54.9915			1.81400			0.907001	+	0.421128i	$0.138366\pi$
$920$	10.9074	−	5.19924i	0.359605	−	0.171414i
$921$	17.2605			0.568753
$922$			3.16710i			0.104303i
$923$			0.517124i			0.0170213i
$924$	17.7065			0.582500
$925$	−5.76419	−	4.67246i	−0.189525	−	0.153630i
$926$	6.44719			0.211868
$927$		−	12.4091i		−	0.407570i
$928$			5.83998i			0.191707i
$929$	−17.4617			−0.572901			−0.286450	−	0.958095i	$-0.592475\pi$
$929$	−17.4617			−0.572901			−0.286450	+	0.958095i	$0.592475\pi$
$930$	12.6854	−	6.04679i	0.415971	−	0.198282i
$931$	4.88972			0.160254
$932$		−	8.30977i		−	0.272195i
$933$			32.5116i			1.06438i
$934$	5.78066			0.189149
$935$	7.81710	+	16.3993i	0.255646	+	0.536315i
$936$	−1.94050			−0.0634273
$937$			27.4261i			0.895970i	0.894041	+	0.447985i	$0.147858\pi$
$937$			27.4261i			0.895970i	−0.894041	+	0.447985i	$0.852142\pi$
$938$			16.8230i			0.549291i
$939$	−6.26304			−0.204387
$940$	7.45764	+	15.6452i	0.243241	+	0.510291i
$941$	−35.1587			−1.14614			−0.573070	−	0.819506i	$-0.694248\pi$
$941$	−35.1587			−1.14614			−0.573070	+	0.819506i	$0.694248\pi$
$942$			4.87516i			0.158841i
$943$		−	16.7521i		−	0.545524i
$944$	5.40502			0.175918
$945$	−5.61108	+	2.67465i	−0.182529	+	0.0870063i
$946$	−24.9250			−0.810381
$947$		−	44.1438i		−	1.43448i	−0.696827	−	0.717240i	$-0.745405\pi$
$947$		−	44.1438i		−	1.43448i	0.696827	−	0.717240i	$-0.254595\pi$
$948$			14.2453i			0.462666i
$949$	−12.8945			−0.418574
$950$	18.5983	+	15.0758i	0.603408	+	0.489124i
$951$	−18.8523			−0.611328
$952$			13.1669i			0.426743i
$953$			27.3169i			0.884881i	0.896798	+	0.442441i	$0.145887\pi$
$953$			27.3169i			0.884881i	−0.896798	+	0.442441i	$0.854113\pi$
$954$	8.39698			0.271862
$955$	1.81027	−	0.862907i	0.0585790	−	0.0279230i
$956$	−10.3068			−0.333345
$957$			4.26814i			0.137969i
$958$			4.72346i			0.152608i
$959$	−0.666567			−0.0215246
$960$	1.67158	+	3.50676i	0.0539499	+	0.113180i
$961$	46.8031			1.50978
$962$		−	0.824585i		−	0.0265857i
$963$		−	17.5579i		−	0.565797i
$964$	−37.6056			−1.21120
$965$	−10.0551	−	21.0943i	−0.323685	−	0.679051i
$966$	4.30130			0.138392
$967$			54.3910i			1.74910i	0.484939	+	0.874548i	$0.338842\pi$
$967$			54.3910i			1.74910i	−0.484939	+	0.874548i	$0.661158\pi$
$968$		−	17.9579i		−	0.577190i
$969$	−12.7925			−0.410954
$970$	1.36913	−	0.652628i	0.0439602	−	0.0209546i
$971$	−14.2906			−0.458606			−0.229303	−	0.973355i	$-0.573645\pi$
$971$	−14.2906			−0.458606			−0.229303	+	0.973355i	$0.573645\pi$
$972$		−	1.49235i		−	0.0478672i
$973$			47.3283i			1.51728i
$974$	−20.8082			−0.666737
$975$	2.45539	−	3.02910i	0.0786355	−	0.0970087i
$976$	−6.36086			−0.203606
$977$		−	8.94905i		−	0.286306i	−0.989701	−	0.143153i	$-0.954276\pi$
$977$		−	8.94905i		−	0.286306i	0.989701	−	0.143153i	$-0.0457240\pi$
$978$			10.0107i			0.320107i
$979$	23.3374			0.745868
$980$	−2.19173	+	1.04474i	−0.0700122	+	0.0333729i
$981$	1.00973			0.0322382
$982$			3.08128i			0.0983277i
$983$			22.1981i			0.708010i	0.935244	+	0.354005i	$0.115180\pi$
$983$			22.1981i			0.708010i	−0.935244	+	0.354005i	$0.884820\pi$
$984$	19.1943			0.611893
$985$	−9.21493	−	19.3318i	−0.293612	−	0.615962i
$986$	−1.35626			−0.0431923
$987$			14.4380i			0.459568i
$988$		−	7.82128i		−	0.248828i
$989$	17.7996			0.565995
$990$	2.92594	+	6.13825i	0.0929924	+	0.195086i
$991$	−13.2764			−0.421740			−0.210870	−	0.977514i	$-0.567630\pi$
$991$	−13.2764			−0.421740			−0.210870	+	0.977514i	$0.567630\pi$
$992$			51.5121i			1.63551i
$993$			0.596245i			0.0189212i
$994$	1.31336			0.0416573
$995$	−11.3392	+	5.40507i	−0.359476	+	0.171352i
$996$	−0.0185049			−0.000586349
$997$		−	19.6929i		−	0.623682i	−0.950134	−	0.311841i	$-0.899054\pi$
$997$		−	19.6929i		−	0.623682i	0.950134	−	0.311841i	$-0.100946\pi$
$998$			3.06150i			0.0969102i
$999$	1.48402			0.0469523

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.c.e.349.5	✓	10
3.2	odd	2		1305.2.c.j.784.6		10
5.2	odd	4		2175.2.a.w.1.4		5
5.3	odd	4		2175.2.a.z.1.2		5
5.4	even	2	inner	435.2.c.e.349.6	yes	10
15.2	even	4		6525.2.a.bs.1.2		5
15.8	even	4		6525.2.a.bl.1.4		5
15.14	odd	2		1305.2.c.j.784.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.c.e.349.5	✓	10	1.1	even	1	trivial
435.2.c.e.349.6	yes	10	5.4	even	2	inner
1305.2.c.j.784.5		10	15.14	odd	2
1305.2.c.j.784.6		10	3.2	odd	2
2175.2.a.w.1.4		5	5.2	odd	4
2175.2.a.z.1.2		5	5.3	odd	4
6525.2.a.bl.1.4		5	15.8	even	4
6525.2.a.bs.1.2		5	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.712495i q^{2} -1.00000i q^{3} +1.49235 q^{4} +(2.01848 - 0.962154i) q^{5} -0.712495 q^{6} +2.77986i q^{7} -2.48828i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.712495i q^{2} -1.00000i q^{3} +1.49235 q^{4} +(2.01848 - 0.962154i) q^{5} -0.712495 q^{6} +2.77986i q^{7} -2.48828i q^{8} -1.00000 q^{9} +(-0.685530 - 1.43816i) q^{10} +4.26814 q^{11} -1.49235i q^{12} +0.779856i q^{13} +1.98063 q^{14} +(-0.962154 - 2.01848i) q^{15} +1.21181 q^{16} +1.90354i q^{17} +0.712495i q^{18} -6.72036 q^{19} +(3.01228 - 1.43587i) q^{20} +2.77986 q^{21} -3.04103i q^{22} +2.17168i q^{23} -2.48828 q^{24} +(3.14852 - 3.88418i) q^{25} +0.555643 q^{26} +1.00000i q^{27} +4.14852i q^{28} -1.00000 q^{29} +(-1.43816 + 0.685530i) q^{30} -8.82061 q^{31} -5.83998i q^{32} -4.26814i q^{33} +1.35626 q^{34} +(2.67465 + 5.61108i) q^{35} -1.49235 q^{36} -1.48402i q^{37} +4.78822i q^{38} +0.779856 q^{39} +(-2.39411 - 5.02255i) q^{40} -7.71389 q^{41} -1.98063i q^{42} -8.19624i q^{43} +6.36956 q^{44} +(-2.01848 + 0.962154i) q^{45} +1.54731 q^{46} +5.19381i q^{47} -1.21181i q^{48} -0.727598 q^{49} +(-2.76746 - 2.24330i) q^{50} +1.90354 q^{51} +1.16382i q^{52} -11.7853i q^{53} +0.712495 q^{54} +(8.61515 - 4.10661i) q^{55} +6.91707 q^{56} +6.72036i q^{57} +0.712495i q^{58} +4.46028 q^{59} +(-1.43587 - 3.01228i) q^{60} -5.24905 q^{61} +6.28464i q^{62} -2.77986i q^{63} -1.73733 q^{64} +(0.750341 + 1.57412i) q^{65} -3.04103 q^{66} +8.49375i q^{67} +2.84075i q^{68} +2.17168 q^{69} +(3.99787 - 1.90567i) q^{70} +0.663102 q^{71} +2.48828i q^{72} +16.5345i q^{73} -1.05736 q^{74} +(-3.88418 - 3.14852i) q^{75} -10.0291 q^{76} +11.8648i q^{77} -0.555643i q^{78} -9.54554 q^{79} +(2.44602 - 1.16595i) q^{80} +1.00000 q^{81} +5.49611i q^{82} -0.0123998i q^{83} +4.14852 q^{84} +(1.83150 + 3.84226i) q^{85} -5.83978 q^{86} +1.00000i q^{87} -10.6203i q^{88} +5.46783 q^{89} +(0.685530 + 1.43816i) q^{90} -2.16789 q^{91} +3.24091i q^{92} +8.82061i q^{93} +3.70056 q^{94} +(-13.5649 + 6.46602i) q^{95} -5.83998 q^{96} +0.952006i q^{97} +0.518410i q^{98} -4.26814 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{4} + 6 q^{6} - 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^4 + 6 * q^6 - 10 * q^9	\( 10 q - 10 q^{4} + 6 q^{6} - 10 q^{9} + 4 q^{10} + 24 q^{11} - 12 q^{14} + 2 q^{15} + 2 q^{16} + 4 q^{19} + 8 q^{20} + 16 q^{21} - 18 q^{24} + 2 q^{25} - 10 q^{29} - 18 q^{30} + 4 q^{31} - 8 q^{34} + 2 q^{35} + 10 q^{36} - 4 q^{39} - 14 q^{40} - 28 q^{41} - 40 q^{44} - 12 q^{46} + 14 q^{49} - 12 q^{50} - 6 q^{54} + 2 q^{55} - 4 q^{56} - 8 q^{59} - 2 q^{60} - 24 q^{61} + 18 q^{64} + 6 q^{65} + 28 q^{66} - 16 q^{69} + 20 q^{70} + 60 q^{71} - 4 q^{74} + 12 q^{75} - 88 q^{76} + 36 q^{79} - 30 q^{80} + 10 q^{81} + 12 q^{84} - 14 q^{85} + 60 q^{86} + 44 q^{89} - 4 q^{90} - 24 q^{91} + 100 q^{94} - 36 q^{95} + 2 q^{96} - 24 q^{99}+O(q^{100}) \) 10 * q - 10 * q^4 + 6 * q^6 - 10 * q^9 + 4 * q^10 + 24 * q^11 - 12 * q^14 + 2 * q^15 + 2 * q^16 + 4 * q^19 + 8 * q^20 + 16 * q^21 - 18 * q^24 + 2 * q^25 - 10 * q^29 - 18 * q^30 + 4 * q^31 - 8 * q^34 + 2 * q^35 + 10 * q^36 - 4 * q^39 - 14 * q^40 - 28 * q^41 - 40 * q^44 - 12 * q^46 + 14 * q^49 - 12 * q^50 - 6 * q^54 + 2 * q^55 - 4 * q^56 - 8 * q^59 - 2 * q^60 - 24 * q^61 + 18 * q^64 + 6 * q^65 + 28 * q^66 - 16 * q^69 + 20 * q^70 + 60 * q^71 - 4 * q^74 + 12 * q^75 - 88 * q^76 + 36 * q^79 - 30 * q^80 + 10 * q^81 + 12 * q^84 - 14 * q^85 + 60 * q^86 + 44 * q^89 - 4 * q^90 - 24 * q^91 + 100 * q^94 - 36 * q^95 + 2 * q^96 - 24 * q^99

Introduction

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